Silaprismanes
What are the silicon polyprismanes?
Silicon polyprismanes or [n,m]silaprismanes can be considered as the layered dehydrogenated molecules of cyclosilanes (silicon rings), where m is the number of vertices of a closed silicon ring, and n is the number of layers. For a large n, polysilaprismanes can be considered as the analogs of silicon singlewalled nanotubes with an extremely small crosssection in the form of a regular polygon. Nevertheless, unlike traditional nanotubes, polysilaprismanes have rectangles on their surfaces instead of hexagons. So, the angles between the covalent SiSi bonds are different from the value of 109.5° usual for the sp^{3}hybridized orbitals like in bulk (diamondtype) silicon. Even though the elementary representatives of polysilaprismanes were synthesized long ago in early 2000, unfortunately, to date, there has not been developed a universal method for obtaining these molecular systems. Some elementary silaprismanes one can see in Figure 1.
This webpage contains the results of computer simulation of silicon polyprismanes obtained in the framework of the scientific project “Computer simulation of functional nanomaterials based on silicon polyprismanes with controlled physicochemical characteristics” that is supported by the Russian Science Foundation (Grant No. 187200183).
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Figure 1 – Atomic structures of the elementary silaprismanes obtained at the DFT/B3LYP/6311G(d,p) level of theory: [2,3]silaprismane Si_{6}H_{6} (a), [2,4]silaprismane Si_{8}H_{8} (b), [2,5]silaprismane Si_{10}H_{10} (c), [2,6]silaprismane Si_{12}H_{12} (d), [2,7]silaprismane Si_{14}H_{14} (e), and [2,8]silaprismane Si_{16}H_{16} (f). 
Thermodynamic and kinetic stability of elementary silicon prismanes
First of all, we determine structural characteristics (bond lengths and valence angles) and binding energies of elementary silicon [2,m]prismanes with m = 3 – 8. The calculation of vibrational spectra confirmed that these molecular structures correspond to the energy minima. The binding energies of elementary silaprismanes were calculated. The binding energy was determined as the difference between the total energy of a silicon prismane and the sum of the energies of the isolated constituent atoms, referred to the number of atoms in the system. Prismanes that possesses higher binding energy is more thermodynamically stable and vice versa. It has been obtained that the most thermodynamically stable of the structures considered is the [2,5]prismane Si_{10}H_{10}. For m > 5, the thermodynamic stability of elementary silicon prismanes slightly monotonously decreases. For every elementary silicon prismane considered, a set of quantum chemical descriptors is defined: HOMO and LUMO energies, ionization potential, electron affinity, chemical potential, electronegativity, chemical hardness and softness, electrophilicity index. The dependencies of some of these descriptors a well as the binding energy on the number of vertices of a closed silicon ring are presented in Figure 2. Basing on the analysis of HOMOLUMO gaps, it was found that elementary silicon prismanes can be conditionally referred to widegap semiconductors or isolators.
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Figure 2 – The dependencies of binding energy (a), HOMOLUMO gap (b), hardness (c) and softness (d), chemical potential (e), and electrophilicity (e) on the number of vertices of a closed silicon ring constructing the prismane cage, obtained at the DFT/B3LYP/6311G(d,p) level of theory 
We also determine the possible decomposition channels of the elementary silicon prismanes. It has been found that the main mechanism of the stability loss is the breaking of the SiSi bond either inside the silicon ring forming the prismane (intraplane bond) or the corresponding bond between the rings (interplane bond). Moreover, it was confirmed that the priority decomposition channel for the systems with even m = 4, 6, 8 is the breaking of one of the interplane bonds, whereas for the silaprismanes with odd m = 3, 5, 7 the priority decomposition channel is the breaking of one of the intraplane Si–Si bonds. The examples of these mechanisms one can see as the animations presented in Figure 3.
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Figure 3 – Animated minimum energy path for the decomposition process of the [2,3]silaprismane (a) and [2,4]silaprismane (b). TS denotes the transition state or saddle point 
The minimum energy barrier preventing the decomposition, as a measure of kinetic stability, nonmonotonously depends on m, but for the prismanes formed by the silicon rings with an odd number of atoms m = 5, 7 it is higher than the corresponding value for the prismanes formed by the silicon rings with an even m number – 4, 6, 8. Using the Arrhenius equation the estimation of the lifetime of elementary prismanes was made at room temperature (300 K) and at the temperature of 800 K (see Table 1).
Table 1. Minimum energy barriers preventing the decomposition of [2,m]silaprismanes (E_{a}), corresponding frequency factors (A), lifetimes estimated using the Arrhenius formula at room temperature (τ_{300}) and 800 K (τ_{800}).
Silaprismane  E_{a}, eV  A, s^{1}  τ_{300}, s  τ_{800}, s 
[2,3]silaprismane  0.79  3.75·10^{13}  4.62·10^{1}  2.46·10^{9} 
[2,4]silaprismane  1.46  5.26·10^{13}  7.20·10^{10}  3.13·10^{5} 
[2,5]silaprismane  2.36  1.08·10^{14}  4.67·10^{25}  7.18·10^{0} 
[2,6]silaprismane  1.52  7.42·10^{14}  4.63·10^{10}  5.08·10^{6} 
[2,7]silaprismane  2.57  9,99·10^{13}  1.26·10^{29}  1.46·10^{2} 
[2,8]silaprismane  1.26  1.72·10^{14}  8.35·10^{6}  4.99·10^{7} 
It was obtained that the elementary silicon prismanes possess high kinetic stability: the estimation of their lifetimes at room temperature gives the macroscopic (“infinite”) values, and their lifetimes at 800 K are greater than microseconds. The decomposition products of elementary silicon prismanes are the nanostructures containing various irregular multimembered silicon rings that are formed due to the breaking of the corresponding Si–Si bonds. According to the data obtained, it was concluded that the preferable candidates for the construction of extended systems in the form of silicon polyprismanes are the [2,m]silaprismanes with m = 5 – 7.
The doping effect
It has been found that the substitution of hydrogen atoms in silicon elementary prismanes by the functional groups NO2 and NH2 (and in some cases, CH3) distorts the silicon frame of prismane, and the stability of such compounds depends on the conformer type, in other words, on the relative orientation of the attached radicals. Some substituted elementary prismanes are shown in Figure 4. The calculation of the vibrational spectra of these systems is shown that they cannot be referred to the local energy minima since they are the highorder saddle points.
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Figure 4 – Atomic structures of some doped silaprismanes obtained at the DFT/B3LYP/6311G(d,p) level of theory: Si_{6}(NH_{2})_{6} (a), Si_{8}(NO_{2})_{8} (b), Si_{10}(CH_{3})_{10} (c), Si_{12}F_{12} (d), Si_{14}(NH_{2})_{14} (e), Si_{16}(NO_{2})_{16} (f). 
The use for passivation of the fluorine atoms instead of hydrogens conserves the structure of silaprismanes. In this case, the decay channels have the universal character and coincide with the decay channels of the unsubstituted silaprismanes. Consequently, the search for the transition states was carried out similarly as for the elementary unsubstituted silaprismanes. The geometry of the corresponding transition configurations of unsubstituted prismanes was used as the initial approximation. It was obtained that the minimum energy barrier preventing the decomposition, as a measure of the kinetic stability of doped silaprismanes, is significantly lower than the corresponding values for the unsubstituted systems. Thus, it is confirmed that the doping reduces the kinetic stability of silicon prismanes.
Can sp^{3}silicon be the metal?
Yes, it can!
On the example of the extended silicon polyprismanes, the metallic nature of the sp^{3}hybridized silicon allotropes was discovered for the first time. From the analysis of the band structure and the density of electronic states, and the behavior of the transmission function near the Fermi level, it was found that the [n,5], [n,6], [n,7], and [n,8]silaprismanes belong to the class of metals and are conductors. Moreover, an increase in the thermodynamic stability of silicon [n,5], [n,6], [n,7], and [n,8]prismanes with their effective length growth was confirmed. See the video below for the details.
To understand a metallicity of silicon polyprismanes in detail, we analyze the band structure, density of electronic states, and electronic transmission coefficients of these nanostructures under periodic boundary conditions. The band structures, as well as the densities of the electronic states (DOS) for all systems considered, are presented in Figure 5.
Figure 5  Band structures and densities of electronic states of Si_{5} (a), Si_{6} (b), Si_{7} (c), and Si_{8} (d) polyprismanes.
One can see that the characteristic semiconductor gap is absent for all considered polysilaprismanes. On the contrary, the traditional for metals overlap of the energy bands containing the Fermi level is observed. In the DOS plots, one can find the Van Hove singularities that are characteristic of the quasionedimensional nanostructures. Note that recently, the prediction of a NaSi clathrate structure have been reported. This material can be used as a precursor for obtaining the pure metal bulk silicon phase at ambient pressure. However, the family of silicon polyprismanes is a unique class of 1D metallic silicon compounds.
To confirm the metallic behavior of polysilaprismanes, we calculate the transmission coefficients of electron tunneling through the polysilaprismanes using the PWcond module of Quantum Espresso. The calculation of transmission coefficients is made without the bias voltage. The polysilaprismane is partitioned into a “device” consisting of a supercell with four elementary cells and the left and right “contacts” that are presented by the same supercells as well. According to our calculations, the number of ballistic channels increases with m growth (see Figure 6).
Figure 6  The electronic transmission coefficients of [n,5] (green line), [n,6] (black line), [n,7] (blue line), and [n,8] (red line) polysilaprismanes.
For example, Si_{5} and Si_{6}polyprismanes demonstrate six ballistic channels while Si_{7} and Si_{8}polyprismanes demonstrate ten ballistic channels. Therefore they possess an amount conductance of 6G_{0} and 10G_{0}, respectively, where G_{0}=2e^{2}/h is the conductance quantum (here e is the elementary charge and h is the Plank’s constant). It should be noted that the electronic transmission around the Fermi energy of the common armchair (metallic) carbon nanotubes is sufficiently lower (see video below for details), the semiconducting carbon peapods become metals only under the influence of strong mechanical deformations, and the carbon analogs of silicon polyprismanes are widegap semiconductors.
Metallic nature resistance to mechanical deformations
We analyze how the mechanical stretching and compression affect the electronic properties of gapless polysilaprismanes. The polysilaprismanes are stretched and compressed along their central axes Z (see Figure 7) by ten percent.
Figure 7  The Si_{6}polyprismane supercell containing four interconnected silicon regular hexagons. Symbol D corresponds to the effective diameter of silicon polyprismane, symbols l_{⊥} and l_{} correspond to the interlayer and intralayer SiSi bonds, respectively.
It is found that such mechanical deformations do not open the energy gap. Densities of electronic states (DOS) of Si_{8}polyprismane under ten percent stretching and compression are presented in Figure 7. From Figure 7, one can see that DOS remains finite at the Fermi level under mechanical strain. Thus, the metallicity of polysilaprismanes is resistant to mechanical deformations.
Figure 8  Densities of electronic states of Si_{8}polyprismane under ten percent stretching (a) and compression (b). Redline corresponds to the undeformed silicon polyprismane.
Also, substitutional doping does not affect the metallic nature. We calculated the density of electronic states of Bdoped and Cdoped Si_{5} and Si_{6} polyprismanes. The data are presented in Figure 9 that demonstrates a comparison of the density of electronic states for the doped and unsubstituted Si_{5} and Si_{6} polyprismane. It is shown that the metallicity of Si_{5} polyprismane is retained in the case of both boron and carbon doping. In the case of boron doping, the density of electronic states near the Fermi level decreases in comparison with the case of unsubstituted polyprismane. At the same time, when doped with carbon, the density of electronic states at the Fermi level remains unchanged. Similar results are obtained for the doped Si_{6} polyprismane.
Figure 9  Density of electronic states for (a) Bdoped, (b) Cdoped Si_{5}polyprismane, and (c) Bdoped, (d) Cdoped Si_{6}polyprismane (red line). The gray filled area corresponds to the unsubstituted Si_{5} and Si_{6}polyprismanes.
Superconducting properties of polysilaprismanes
In order to analyze the superconducting properties of silicon polyprismanes, we analyzed the phonon spectrum and phonon density of states of the optimized Si_{5}polyprismane. The resulting phonon spectrum (Figure 10) does not contain negative frequencies for all nonequivalent values of the quasiwave vector, which affects the phonon density of states and indicates the dynamic stability of these compounds.
Figure 10  Phonon density of states of Si_{5}polyprismane.
After calculating the phonons, the spectral function of the electronphonon interaction was obtained (Figure 11).
Figure 11  The frequency dependence α^{2}F(ω) of the spectral function of electronphonon interaction.
This function determined the electronphonon interaction constant. Its value was 1.96. McMillan’s equation was used to find the critical temperature of the polysilaprismane superconducting transition. The obtained critical temperature was 8.8 K. The calculated electronphonon coupling constant and critical temperature obtained as a result of the calculations make it possible to classify polyprismanes as lowtemperature superconductors. The critical temperature values for the silicon polyprismanes correspond to lowtemperature singleelement superconductors, such as Pb(T_{c}≈7.2K), Hg(T_{c}≈4K), Sn(T_{c}≈3.7K).
Elastic properties of polysilaprismanes
Mechanical deformations do not affect the electronic properties of polysilaprismanes strongly. We analyze the mechanical properties of silicon silaprismanes to investigate their response to both tensile and compressive strains along their main axes. We restrict ourselves to rather small strain values (not exceeding 4%) in order to maintain the system in the elastic area. For all considered polysilaprismanes, we estimate Young’s modulus that is defined as the second derivative of the total energy with respect to the strain divided by the equilibrium volume. We obtain Young’s modules 192.8; 149.6; 124.7; 110.7 GPa for the Si_{5}, Si_{6}, Si_{7}, and Si_{8}polyprismanes, respectively. These values are rather high and comparable to the values obtained for some metals and steels as well as for the highstable silicon tubular nanostructures. Also, we compare the obtained Young’s modules with the corresponding values for unsubstituted (160202 GPa) and borondoped (62125 GPa) bulk silicon, silicon nanowires (60240 GPa, the value depends on diameter) and nanofilms (~150 GPa), branched silicon nanowires (0.086 GPa), siliconbased nanotubes (5080 GPa). The experimental value of Young’s modulus for traditional carbon nanotubes is equal to ~1 TPa. Thus, despite the fact that Young’s modulus of polysilaprismanes is rather high and comparable with some steels, it is significantly lower than the corresponding value for carbon nanotubes. Note that if the number of vertices of regular silicon polygons m that make up the polyprismane increases, the value of Young’s modulus reduces. Thus, polysilaprismanes with smaller effective diameters are more resistant to the uniaxial compression and stretching under elastic deformation than the polysilaprismanes with larger effective diameters.
How to obtain the silicon polyprismanes?
Taking into account that some elementary silicon prismanes have already been synthesized, one of the possible hypothetical methods for producing “long” samples can be carried out using convergent synthesis mechanisms (see Figure 12) with correctly selected catalysts and functional binding molecular bridges.
Figure 12  Hypothetical reaction of the convergent synthesis of higher [4,6]silaprismane from two elementary [2,6]silaprismanes by covalent bonding via the SiO_{2} molecular bridges.
In addition, it seems possible to obtain silicon polyprismanes by growing on the surface of a silicene substrate by molecular beam epitaxy (see Figure 13). In the process of epitaxy, covalent bonds will be formed perpendicular to the central axis of the polyprismane, ensuring the vertical growth of the nanostructure. Since the “ideal” silicene consists of sixmembered silicon rings, by default, only Si_{6} polyprismanes can be obtained.
Figure 13  Hypothetical reaction of epitaxial production of higher [n,6]silaprismanes on the silicene/metal substrate: general scheme (left) and a frame of direct molecular dynamics modeling (right).
However, initiating the formation of a sequence of StoneWales type defects in silicene (most likely, silicene deposited on a metal substrate will contain similar and other defects), Si_{5} and other polyprismanes can also be obtained. It is possible that obtaining silicon polyprismanes in the form of molecular or covalent crystals, and not in the gas phase, will be more promising. Such crystalline compounds can hypothetically be obtained using ultrahigh pressures from precursors containing silicon nanotubes and closed fullerenelike frameworks.
Application prospectives of silaprismanes
For a long time to the present days, diamondtype silicon is the basis of modern consumer and special purpose electronics. However, the active development of nanotechnologies makes it possible to think about the use of silicon in new forms, for example, in the form of polyprismanes, which can qualitatively improve the component base of modern electronic devices. The extraordinary electronic properties of silicon polyprismanes together with their structural and mechanical characteristics make them potentially suitable in the various fields of nextgen technologies. Building the next generation of technological processes is impossible without the use of an improved material base. For example, the miniaturization of electronics inevitably leads to the using of appropriate semiconductor or metallic nanomaterials, which will provide in the future a significant increase in the speed of computing systems. Extended molecules of silicon polyprismanes may be the ultrathin functional nanowires with controlled electronic characteristics and can be used in elements of computational logic. According to our studies, they are potentially good conductors. Encapsulation the metastable nanostructures (for example, nitrogen chains) inside the higher silicon polyprismanes can stabilize the latter, which will make it possible to obtain an effective highenergy material.
Furthermore, high electrophilicity of polyprismanes indicates the possibility of including the charged ions inside their structure that might be useful in biological and medical applications as drug delivery systems. Also, silicon polyprismanes can be used for storing and transporting hydrogen instead of carbon nanomaterials traditionally offered in the literature for these purposes. Their conductive properties will allow one to use the polysilaprismanes as the elements of measuring equipment, for example, tips of a scanning tunneling microscope. Also, the absence of free covalent bonds makes them insensitive to environmental pollutants (free radicals), which reduces the reactivity of the silicon needle, allowing one to achieve the atomic resolutions in the microscope.
Videomaterials
Publications
For detailed information, see the following publications:
1. Gimaldinova M.A., Katin K.P., Salem M.A., Maslov M.M. Energy and electronic characteristics of silicon polyprismanes: density functional theory study // Letters on Materials. 2018. V. 8. P. 454457. DOI: 10.22226/2410353520184454457
2. Grishakov K.S., Katin K.P., Maslov M.M. The Effects of Doping on the Electronic Characteristics and Adsorption Behavior of Silicon Polyprismanes // Computation. 2020. V. 8. P. 25. DOI: 10.3390/computation8020025
3. Maslov M.M., Grishakov K.S., Gimaldinova M.A., Katin K.P. Carbon vs silicon polyprismanes: a comparative study of metallic sp3hybridized allotropes // Fullerenes, Nanotubes and Carbon Nanostructures. 2020. V. 28. P. 97103. DOI: 10.1080/1536383x.2019.1680974
4. Katin K.P., Grishakov K.S., Gimaldinova M.A., Maslov M.M. Silicon rebirth: Ab initio prediction of metallic sp3hybridized silicon allotropes // Computational Materials Science. 2020. V. 174. P. 109480. DOI: 10.1016/j.commatsci.2019.109480
5. Gimaldinova M.A., Kochaev A.I., Maslov M.M. Ab initio modeling of dynamic stability of silicon prismanes // Letters on Materials. 2020. In press.
6. Salem M.A., Gimaldinova M.A., Kochaev A.I., Maslov M.M. Doping effect on electronic structure and optical properties of silicon biprismanes: DFT and TDDFT studies // Letters on Materials. 2020. In press.
Conferences
1. Materials science of the future: Research, development, scientific training (MSF’2019), 1214 February, 2019, Nizhny Novgorod, Russia. Oral presentation “Silicon polyprismanes: Insight from ab initio calculations”.
2. 14^{th} International Conference Advanced Carbon NanoStructures (ACNS’2019), 15 July, 2019, SaintPetersburg, Russia. Poster presentation “Carbon vs silicon polyprismanes: A density functional theory study”.
3. III International SchoolConference Applied Nanotechnology and Nanotoxicology (ANT2019), 1013 October, 2019, Sochi, Russia. Poster presentations: “Metallicity of Silicon: Ab Initio Study of sp^{3}Hybridized Silicon Allotropes” and “High Kinetic Stability of Silicon Prismanes: Density Functional Theory Study”.
Acknowledgments
The presented study was performed with the financial support of the Russian Science Foundation (Grant No. 187200183). We are grateful to DSEPYRI for the organizational support and computational resources provision.